An appropriate framework is put forward for the construction of
$\lambda$-models with $\infty$-groupoid structure, which we call
\textit{homotopic $\lambda$-models} through the use of an $\infty$-bicategory
with cartesian closure and enough points. With this, we establish the start of
a project of generalization of Domain Theory and $\lambda$-calculus, in the
sense that the concept of proof (path) of equality of $\lambda$-terms is raised
to \textit{higher proof} (homotopy)